[itex]2^{2} = 2 + 2[/itex](adsbygoogle = window.adsbygoogle || []).push({});

[itex]3^{2} = 3 + 3 + 3[/itex]

[itex]4^{2} = 4 + 4 + 4 + 4[/itex]

Generalizing...

[itex]x^{2} = x + ... + x[/itex] (x times)

Take the derivative of both sides.

[itex]\frac{\delta}{\delta x} x^{2}[/itex] = [itex]\frac{\delta}{\delta x}[ x + ... + x][/itex] (x times)

[itex]2x = 1 + ... + 1[/itex] (x times) [itex]= x [/itex] !?

Surely, there must be something wrong... and there is! But I thought this was pretty cool.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Simple derivative. Where is the logical fallacy here?

**Physics Forums | Science Articles, Homework Help, Discussion**